We formulate an optimum-taxation model, where parents leave bequests to their descendants for altruistic reasons. In contrast to the standard model, individuals differ not only in earning abilities, but also in initial (inherited) wealth. In this model a redistributive motive for an inheritance tax - which is equivalent to a uniform tax on all expenditures - arises, given that initial wealth increases with earning abilities. Its introduction increases intertemporal social welfare or has an ambiguous effect, depending on whether the bequeathing generation can adjust their behaviour and whether the external effect related to altruism is accounted for in the social objective.